09a 5 mm1f_methods_unit_1f_-_november_2012

Centre Number Candidate Number

Write your name hereSurname Other names

Total Marks

Paper Reference

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P40676A©2012 Pearson Education Ltd.

6/6/7/

*P40676A0124*

Edexcel GCSE

Methods in MathematicsUnit 1: Methods 1For Approved Pilot Centres ONLY

Foundation TierMonday 12 November 2012 – MorningTime: 1 hour 45 minutes 5MM1F/01You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser. Tracing paper may be used.

Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name,

centre number and candidate number. Answer all questions. Answer the questions in the spaces provided

– there may be more space than you need. Calculators must not be used.

Information The total mark for this paper is 100 The marks for each question are shown in brackets

– use this as a guide as to how much time to spend on each question. Questions labelled with an asterisk (*) are ones where the quality of your

written communication will be assessed.

Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end.

2

*P40676A0224*

GCSE Mathematics 2MM01

Formulae: Foundation Tier

You must not write on this formulae page.Anything you write on this formulae page will gain NO credit.

Area of trapezium = 12 (a + b)h

Volume of prism = area of cross section × length

b

a

h

length

sectioncross

3

*P40676A0324* Turn over

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

You must NOT use a calculator.

1 (a) Write the number four thousand, seven hundred and thirty six in figures.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Write the number 23584 correct to the nearest hundred.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(Total for Question 1 is 2 marks)

2 The shaded shape is drawn on a centimetre square grid.

Reflect the shaded shape in the mirror line.


Mirror line

4

*P40676A0424*

3 The diagram shows a quadrilateral.

(a) What is the mathematical name for this quadrilateral?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Write down the type of angle shown by the letter

(i) x

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) y

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


4 Write the fraction 1824

in its simplest form.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


x

y

5


5 Here is a spinner.

The arrow on the spinner can stop on blue or on yellow or on red. Amy is going to spin the arrow once.

impossible unlikely even likely certain

Choose a word from the box to best describe the probability

(a) that the arrow will stop on yellow,

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) that the arrow will stop on red,

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) that the arrow will stop on pink.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)


yellow

red

yellow

blue

6

*P40676A0624*

6 Here is a list of 7 numbers.

7 8 9 16 17 18 24

From the list,

(a) write down a square number

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) write down a multiple of 6

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) write down a cube number.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)


7 (a) Work out 3 × 4 – 2

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Work out 40 ÷ (14 – 6)

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) Work out 15 + 10 ÷ 5

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)


7


8 Here are 6 rectangles drawn on a square grid.

(a) Write down the letters of the two congruent rectangles.

.. . . . . . . . . . . . . . . . . . . . and .. . . . . . . . . . . . . . . . . . .

(1)

Here are 5 triangles drawn on a square grid.

(b) Write down the letters of the two similar triangles.

.. . . . . . . . . . . . . . . . . . . . and .. . . . . . . . . . . . . . . . . . .

(1)


A

FED

CB

J

L

K

H

G

8

*P40676A0824*

9 (a) Draw all the lines of symmetry on this diagram.

(2)

(b) This shape has rotational symmetry.

Write down the order of rotational symmetry.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)


9


10 (a) Work out 4 × 300

... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Work out 64 ÷ 4

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) Work out –8 + 10

... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(d) Work out 561 × 34

... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)


10

*P40676A01024*

11 There are 8 beads in a bag.

4 beads are red. 1 bead is white. 3 beads are blue.

Jane takes at random a bead from the bag.

(a) On the probability scale, mark with a cross (×) the probability that Jane takes a white bead.

(1)

(b) On the probability scale, mark with a cross (×) the probability that Jane takes a green bead.

(1)

(c) On the probability scale, mark with a cross (×) the probability that Jane takes a red bead.

(1)


0 112

0 112

0 112

11


12 Here are four cards. There is a number on each card.

(a) Use each of the four cards once to make the smallest 4 digit number.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Use each of the four cards once to make the largest 4 digit even number.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) Use two cards to make a fraction equivalent to 23

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(d) Use two cards to make a fraction greater than 12

and less than 1

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)


6 4 3 7

12

*P40676A01224*

13 Pippa rolls an ordinary fair dice once.

(a) Write down the probability that she gets

(i) the number 3

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) an even number

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iii) a number greater than 4

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)

Pete rolls an ordinary fair dice once and throws a fair coin once.

(b) (i) Write down all the possible outcomes.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) Write down the probability that Pete gets a 6 and a Head.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)


13


14 (a) Write these numbers in order of size. Start with the smallest number.

6 –3 17 –5 2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Write these numbers in order of size. Start with the smallest number.

0.67 0.078 0.6 0.75 0.705

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) Write these numbers in order of size. Start with the smallest number.

12

310

34

25

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


14

*P40676A01424*

15 (a) Simplify b + b + b + b

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Simplify 3 × c × d

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) Simplify 4h – 2r + 3h + 7r

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


16 (a) Work out 38

+ 28

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Work out 710

– 35

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(c) Work out 58

÷ 34

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


15


17 Here is a sequence of patterns made from sticks.

(a) Complete the table to show the number of sticks in each pattern.

Pattern number 1 2 3 4 5

Number of sticks 7 12 17 22... . . . . . . . . . . . . . . . . . . .

(1)

(b) Find the number of sticks in Pattern number 8

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) Find an expression in terms of n for the number of sticks in Pattern number n.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

Ali has 60 sticks. She wants to use as many sticks as possible to make a Pattern number.

(d) What is the largest Pattern number she can make?

... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


Pattern number 1 Pattern number 2

Pattern number 4Pattern number 3

16

*P40676A01624*

18 (a) Solve x + 4 = 16

x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Solve 5b = 30

b = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) Solve 7y – 5 = 16

y = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


19 Which is the larger, 26 or 62 ?

You must show your working.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


17


20 The Venn diagram shows the numbers from 1 to 15

(a) Use one word to complete this sentence.

All the numbers in set B are . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . of 12(1)

(b) Write down the numbers that are in set A and also in set B.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) Find P(A��

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


15

10

12

1

7

3

2

13

511

9

B

14

8A

4

6

18

*P40676A01824*

21

(a) Write down the coordinates of point C.

(. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)(1)

(b) Find the coordinates of point D so that ABCD is a parallelogram.

(. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)(1)

E is another point on the grid. The midpoint of AE has coordinates (2, 6)

(c) Find the coordinates of point E.

(. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)(2)


10

9

8

7

6

5

4

3

2

1

–1

y

–2

O–2 –1 1 2 3 4 5 6 7 8 9 10 x

C

B

A

19


22 Here is a rectangle.

The rectangle has a width of 4 cm. It has a perimeter of 28 cm.

(a) Work out the area of the rectangle.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2

(3)

A square has an area of 81 cm2.

(b) Work out the perimeter of the square.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm(3)


Diagram NOT accurately drawn

4 cm

20

*P40676A02024*

23 Ramesh throws a biased coin. The probability that the coin will land on a Head is 0.37

(a) Write down the probability that the coin will land on a Tail.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

Ramesh is going to throw the coin 500 times.

(b) Work out an estimate for the number of times that the coin will land on a Head.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


24* Work out the area of the shaded shape.


10 cm

8 cm

4 cm

3 cm


21


25 On the grid, draw the graph of y = 2x + 3 for values of x from –2 to 2


22

*P40676A02224*

26*

ABC and ABD are right-angled triangles. BCDE is a straight line.

Angle BAC = 35° Angle ADE = 150°

Work out the size of angle y. Give reasons for your answer.


B

150°

y

EDC

A

35°


23

*P40676A02324*

27

Describe fully the single transformation that maps shape P onto shape Q.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


TOTAL FOR PAPER IS 100 MARKS

y

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

O–1–2–3–4–5–6 1 2 3 4 5 6 x

P

Q

24

*P40676A02424*

BLANK PAGE

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09a 5 mm1f_methods_unit_1f_-_november_2012